B样条曲面在严格约束状态下的光顺拟合

提出一种新的B样条曲面造型方法:光顺地拟合空间型值点且同时严格地通过其中部分点.运用Lagrange乘子的条件极值法并引入光顺加权项，求出位置偏离和形状弯曲的最小二乘解，可以得到被称为B样条光顺准拟合的良好造型曲面.这一方法在包含门窗的交通工具外壳曲面设计、机械产品装配联接件制造中具有明显的实用价值.     

自适应乘子在工程优化问题中的应用

在增广Lagrange乘子函数和协作进化算法的基础上,采用自适应策略来解决工程优化问题.其中存在两组相互作用的进化种群A和B,A利用B的反馈信息来评价A中乘子个体的优劣,进而进化A中乘子个体;B则利用A中乘子个体来动态进化原问题的候选解个体.在算法迭代过程中,罚因子是确定性逐渐增大,以使算法逐渐收敛;A中乘子个体则朝其最优值的方向进化,且由B可得到原问题的最优解.与基于静态和动态罚函数的GAs相比,该算法准确度和鲁棒性较高,易于实现,并适合并行化计算.     

自适应乘子在工程优化问题中的应用

在增广Lagrange乘子函数和协作进化算法的基础上，采用自适应策略来解决工程优化问题。其中存在两组相互作用的进货种群A和B，A利用B的反馈信息来评价A中乘子个体的优劣，进而进化A中乘子个体；B则利用A中乘子个体来动态进化原问题的候选解个体。在算法迭代过程中，罚因子是确定性逐渐增大，以使算法逐渐收敛；A中乘子个体则朝其最优值的方向进化，且由B可得到原问题的最优解。与基于静态和动态罚函数的GAs相比，该算法准确度和鲁棒性较高，易于实现，并适合并行化计算。     

不依赖于量化参数的视频编码控制优化技术

目前,混合式视频编码技术普遍采用基于量化参数的Lagrange乘子优化算法(QP-L)实现预测编码的率失真优化计算.文中则提出一种新的率失真优化算法Adapt-L,可以根据视频信号的率失真统计特性,自适应地调整Lagrange乘子的计算.实验及数据分析表明,在QP-L算法的Lagrange乘子和视频信号的率失真统计信息...     

基于B-样条曲线的线缆变形仿真

线缆变形仿真是线缆辅助设计和维修过程仿真需要解决的核心问题,也是目前虚拟现实技术研究的热点之一。B-样条曲线是计算几何学的重要理论成果,已经广泛应用于计算机辅助设计。本文首先对B-样条函数的概念进行了简单介绍,分析了用三次开放B-样条曲线进行线缆变形仿真的优越性;然后将全局能量优化方法与高度坐标置零法结合求解曲线控制点的坐标,建立关于已知两端点位置和通过指定点的线缆模型;用Lagrange乘子法建立指定点有切矢约束的线缆模型。这种方法描述的是处于平衡状态的线缆变形,计算量小,模型逼真,而且形状控制方便,能够实现线缆布线指导和维修过程仿真。     

三维图像重构的参数估计与算法实现

论文介绍了一种SFS算法的参数估计及其实现。它在考虑自遮掩影响的情况下,有效地估计了SFS算法中涉及的各种控制参数,并引入亮度约束、灰度梯度约束和可积性约束,计算出表面高度和表面向量,实现三维重构。最后还指出了在Matlab中实现需要注意的问题。     

改进Lagrange乘子法及收敛性分析

将与不等式约束相关的乘子重新定义为原乘子的正定函数,则Karush-Kuhn-Tucker必要条件中关于不等式约束乘子的非负约束可以去掉,并能构造出直接处理不等式约束的Lagrange乘子法.分析了算法的收敛性,利用LaSalle不变集原理揭示其稳定机制,并讨论如何减弱收敛条件和扩大收敛域.     

基于明暗恢复法的三维重建算法分析

明暗恢复形状法是计算机视觉领域的热门问题。明暗恢复法是通过一张照片的灰度信息恢复物体表面形状的一种方法。本文从数学角度度分析了SFS问题,并提出了三种解法:直接法求解,变分法求解和采用优化理论理论求解。并分析比较了这三种方法的适用范围和各自的典型算法。最后分析了SFS问题的发展趋势和难点问题。     

一种新的非线性规划神经网络模型

提出一种新型的求解非线性规划问题的神经网络模型.该模型由变量神经元、Lagrange乘子神经元和Kuhn-Tucker乘子神经元相互连接构成.通过将Kuhn-Tucker乘子神经元限制在单边饱和工作方式,使得在处理非线性规划问题中不等式约束时不需要引入松弛变量,避免了由于引入松弛变量而造成神经元数目的增加,有利于神经网络的硬件实现和提高神经网络的收敛速度.可以证明,在适当的条件下,文中提出的神经网络模型的状态轨迹收敛到与非线性规划问题的最优解相对应的平衡点.     

分形插值在风速时间序列中的应用

针对风电场风速数据中大量连续缺失数据的插值问题,提出了一种基于自适应变异粒子群优化（PSO）的分形插值算法。首先,在粒子群优化算法中引入变异因子,增强粒子的多样性,提高算法搜索精度;其次,通过自适应变异粒子群优化算法来得到分形插值算法中垂直比例因子参数的最佳取值;最后,对两组不同趋势和变化特征的数据集进行分形插值计算分析,并把所提算法与Lagrange插值和三次样条插值方法进行对比。结果表明：分形插值不仅可以保持风速曲线的整体波动特性和局部特征,而且比传统插值方法的精度更高;在基于Dataset A的实验中,分形插值的均方根误差（RMSE）分别比Lagrange插值和三次样条插值减小了66.52%和58.57%;在基于Dataset B的实验中,分形插值的RMSE分别比Lagrange插值和三次样条插值减小了76.72%和67.33%。证明分形插值更适合连续缺失且波动强烈的风速时间序列的插值。     

Lofted B-spline surface interpolation by linearly constrained energy minimization

This paper proposes a new approach for lofted B-spline surface interpolation to serial contours, where the number of points varies from contour to contour. The approach first finds a common knot vector consisting of fewer knots that contain enough degrees of freedom to guarantee the existence of a B-spline curve interpolating each contour. Then, it computes from the contours a set of compatible B-spline curves defined on the knot vector by adopting B-spline curve interpolation based on linearly constrained energy minimization. Finally, it generates a B-spline surface interpolating the curves via B-spline surface lofting. As the energy functional is quadratic, the energy minimization problem leads to that of solving a linear system. The proposed approach is efficient in computation and can realize more efficient data reduction than previous approaches while providing visually pleasing B-spline surfaces. Moreover, the approach works well on measured data with noise. Some experimental results demonstrate its usefulness and quality.     

Quadratic B-spline curve interpolation

Traditional approach in performing even-degree B-spline curve/surface interpolation would generate undesired results. In this paper, we show that the problem is with the selection of interpolation parameter values, not with even-degree B-spline curves and surfaces themselves. We prove this by providing a new approach to perform quadratic B-spline curve interpolation. This approach generates quadratic B-spline curves whose quality is comparable to that of cubic interpolating B-spline curves. This makes quadratic B-spline curves better choices than cubic B-spline curves in some applications in graphics and geometric modeling, since it is cheaper to render/subdivide a quadratic curve and it is easier to find the intersection of two quadratic curves.     

B-spline surface fitting based on adaptive knot placement using dominant columns

By expanding the idea of B-spline curve fitting using dominant points (Park and Lee 2007 [13]), we propose a new approach to B-spline surface fitting to rectangular grid points, which is based on adaptive knot placement using dominant columns along u- and v-directions. The approach basically takes approximate B-spline surface lofting which performs adaptive multiple B-spline curve fitting along and across rows of the grid points to construct a resulting B-spline surface. In multiple B-spline curve fitting, rows of points are fitted by compatible B-spline curves with a common knot vector whose knots are computed by averaging the parameter values of dominant columns selected from the points. We address how to select dominant columns which play a key role in realizing adaptive knot placement and thereby yielding better surface fitting. Some examples demonstrate the usefulness and quality of the proposed approach.     

An Algorithm for Direct Multiplication of B-Splines

B-spline multiplication, that is, finding the coefficients of the product B-spline of two given B-splines is useful as an end result, in addition to being an important prerequisite component to many other symbolic computation operations on B-splines. Algorithms for B-spline multiplication standardly use indirect approaches such as nodal interpolation or computing the product of each set of polynomial pieces using various bases. The original direct approach is complicated. B-spline blossoming provides another direct approach that can be straightforwardly translated from mathematical equation to implementation; however, the algorithm does not scale well with degree or dimension of the subject tensor product B-splines. To addresses the difficulties mentioned heretofore, we present the Sliding Windows Algorithm (SWA), a new blossoming based algorithm for the multiplication of two B-spline curves, two B-spline surfaces, or any two general multivariate B-splines.      

用LS-SVMs整体构造B样条曲线

由给定的空间数据点集构造B样条曲线是CAGD中一个重要研究课题,常用的逼近方法实质上是基于“经验风险”意义下的最小二乘逼近。文章讨论了基于“结构风险”意义下用最小二乘支持向量回归机整体构造B样条曲线的逼近问题,其出发点是最小化结构风险,而不是传统学习的经验风险最小化,从而在理论上保证了好的推广能力,能够实现对原始曲线的逼近而不仅仅是对测量数据点的逼近。文章建立了B样条曲线拟合的数学模型,并构造了一种特殊的核函数来保证曲线的B样条表示形式。该方法为曲线拟合问题提供了新思路,数值实验证实了可行性。     

基于双正交非均匀B样条小波的曲线逼近方法

针对B样条曲线逼近有序数据点在应用最小二乘法时出现的计算量较大问题,提出一种基于双正交非均匀B样条小波的曲线逼近方法。其基本思想是：先用最小二乘法生成初始B样条逼近曲线,再用细节曲线逼近误差向量,接着将细节曲线叠加于原逼近曲线得到新的B样条曲线,这个过程是迭代的。细节曲线的基函数是双正交非均匀B样条小波。与传统最小二乘法相比,该方法仅需计算新增线性系统,避免重复计算原系统,降低了计算量,提高了运算效率;此外,给出了B样条逼近曲线的一种多分辨率表示形式。     

Approximate merging of B-spline curves via knot adjustment and constrained optimization

This paper addresses the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. The basic idea of the approach is to find the conditions for precise merging of two B-spline curves, and perturb the control points of the curves by constrained optimization subject to satisfying these conditions. To obtain a merged curve without superfluous knots, we present a new knot adjustment algorithm for adjusting the end k knots of a kth order B-spline curve without changing its shape. The more general problem of merging curves to pass through some target points is also discussed.     

Cubic B-spline curve approximation by curve unclamping

A new approach for cubic B-spline curve approximation is presented. The method produces an approximation cubic B-spline curve tangent to a given curve at a set of selected positions, called tangent points, in a piecewise manner starting from a seed segment. A heuristic method is provided to select the tangent points. The first segment of the approximation cubic B-spline curve can be obtained using an inner point interpolation method, least-squares method or geometric Hermite method as a seed segment. The approximation curve is further extended to other tangent points one by one by curve unclamping. New tangent points can also be added, if necessary, by using the concept of the minimum shape deformation angle of an inner point for better approximation. Numerical examples show that the new method is effective in approximating a given curve and is efficient in computation.     

外载荷的B样条曲线变形

运用能量优化的思想,提出一种B样条曲线变形的新方法,可用于B样条曲线的变形。首先将B样条曲线段类比为有限单元法中线单元,并将作用在B样条曲线段的外载荷等效成线单元的端点力,分别建立B样条曲线内部能量、外载荷能量函数方程;外载荷的改变将引起B样条曲线能量的变化,通过求解一个使曲线能量的变化量为最小的优化问题,得到变形后的B样条曲线。运用该方法实现了B样条曲线的局部、整体等变形操作。     

Shape modeling based on specifying the initial B-spline curve and scaled BFGS optimization method

In this paper, we consider the problem of fitting the B-spline curves to a set of ordered points, by finding the control points and the location parameters. The presented method takes two main steps: specifying initial B-spline curve and optimization. The method determines the number and the position of control points such that the initial B-spline curve is very close to the target curve. The proposed method introduces a length parameter in which this allows us to adjust the number of the control points and increases the precision of the initial B-spline curve. Afterwards, the scaled BFGS algorithm is used to optimize the control points and the foot points simultaneously and generates the final curve. Furthermore, we present a new procedure to insert a new control point and repeat the optimization method, if it is necessary to modify the fitting accuracy of the generated B-spline fitting curve. Associated examples are also offered to show that the proposed approach performs accurately for complex shapes with a large number of data points and is able to generate a precise fitting curve with a high degree of approximation.